One of the stock arguments used to justify income inequality is the incentive argument. The gist is that income inequality is necessary as a motivating factor—crudely put, if people could not get (very) rich, then they would not have the incentive to do such things as work hard, innovate, invent and so on. The argument requires the assumption that hard work, innovation, inventing and so on are good; an assumption that has a certain general plausibility.
This argument does have considerable appeal. In terms of psychology, it is reasonable to make the descriptive claim that people are primarily motivated by the possibility of gain (and also glory). This view was held by Thomas Hobbes and numerous other thinkers on the grounds that it does match the observed behavior of many (but not all) people. If this view is correct, then achieving the goods of hard work, innovation, invention and so on would require income inequality.
There is, of course, the counter that some people seem to be very motivated by factors other than achieving an inequality in financial gain. Some are motivated by altruism, by a desire to improve, by curiosity, by the love of invention, by the desire to create things of beauty, to solve problems and so many other motives that do not depend on income. These sort of motivations do suggest that income inequality is not necessary as a motivating factor—at least for some people.
Since this is a matter of fact regarding human psychology, it is something that can (in theory) be settled by the right sort of empirical research. It is well worth noting that even if income inequality is necessary as a motivating factor, there remain many other concerns, such as the question of how much income inequality is necessary (and also how much is morally acceptable).
Interestingly, the incentive argument is something of a two-edged sword: while it can be used to justify income inequality, it can also be used to argue against the sort of economic inequality that exists in the United States and almost all other countries. The argument is as follows.
While worker productivity has increased significantly in the United States (and other countries) income for workers has not matched this productivity. This is a change from the past—income of workers went up more proportionally to the increase in productivity. This explains, in part, why CEO (and upper management in general) salaries have seen a significant increase relative to the income of workers: the increased productivity of the workers generates more income for the upper management than it does for the workers doing the work.
If it is assumed that gain is necessary for motivation and that inequality is justified by the results (working harder, innovating, producing and so on), then the workers should receive a greater proportion of the returns on their productivity. After all, if high executive compensation is justified on the grounds of its motivation in regards to productivity, innovation and so on, then the same principle would also apply to the workers. They, too, should receive compensation proportional to their productivity, innovation and so on. If they do not, then the incentive argument would entail that they would not have the incentive to be as productive, etc.
It could, of course, be argued, that top management earns its higher income by being primarily responsible for the increase in worker productivity—that is, the increase in worker productivity is not because of the workers but because of the leadership which is motivated by the possibility of gain on the part of the leadership. If this is the case, then the disparity would be fully justified by the incentive argument: the workers are more productive because the CEO is motivated to make them more productive so she can have even greater income.
However, if the increased productivity is due mainly to the workers, then this seems to counter the incentive argument: if workers are more productive than before with less relative compensation, then there does not seem to be that alleged critical connection between incentive and productivity required by the incentive argument. That is, if workers will increase productivity while receiving less compensation relative to their productivity, then the same would presumably hold for the top executives. While there are many other ways to warrant extreme income inequality, the incentive argument does seem to have a problem.
One possible response is to argue for important differences between the executives and workers such that executives need the incentive provided by the extreme inequality and workers are motivated sufficiently by other factors (like being able to buy food). It could also be contended that the workers are motivated by the extreme inequality as well—they would not be as productive if they did not have the (almost certainly false) belief that they will become rich.